Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5142 | C2 | semidirect |
| 2. #83799 | C2 | semidirect |
| 3. C22×D48 | C2 | semidirect |
| 4. C2×C3×#350 | C2 | semidirect |
| 5. C2×#4516 | C2 | semidirect |
| 6. #71440 | C2 | semidirect |
| 7. #67807 | C2 | semidirect |
| 35. C2×#350 | D3 | semidirect |
| 69. C2×D24 | D4 | semidirect |
| 75. C2×C3×C16 | D4 | semidirect |
| 79. #819 | D4 | semidirect |
| 199. C2×C16 | #67 | semidirect |
| 391. C3 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5142 | 2 |
| #83799 | 2 |
| C22×D48 | 2 |
| C2×C3×#350 | 2 |
| C2×#4516 | 2 |
| #71440 | 2 |
| #67807 | 2 |
| #13319 | 3 |